A (proper) vertex-colouring of \(G\)  is an assignment of colours to the vertices of \(G\)  such that adjacent vertices receive different colours. If \(G\)  can be properly coloured using \(n\)  colours, we say that \(G\)  is \(n\) -colourable. The chromatic number \(\chi (G)\)  of \(G\)  is the least number of colours required such that \(G\)  has a proper colouring. A variant of the chromatic number is the fractional chromatic number, where in fractional colouring the vertices of a graph \(G\)  are assigned a set of colours instead of a single colour. More formally, the definitions of fractional colouring and fractional chromatic number that we adopt are those used in [1]} and presented here in Definition .
